An Estimation of the Cost and Welfare of the
new Colombian Healthcare Plan
Alvaro J. Riascos
∗Sergio A. Camelo
†Universidad de los Andes and Quantil
June 15, 2014
∗Economics Faculty. E-mail: ariascos@uniandes.edu.co. Address: Facultad de Econom´ıa, Universidad de los Andes. Carrera 1A 18A - 70 Bloque C, Bogot´a DC.
†Economics Faculty and Mathematics Department. E-mail: sa.camelo38@uniandes.edu.co. Address: Facultad de Econom´ıa, Universidad de los Andes. Carrera 1A 18A - 70 Bloque C, Bogot´a DC.
Abstract
This article estimates the expected cost and welfare of the new benefits plan in Colombian health care. The analysis starts out on the basis that by reducing barriers to claims for services that are cur-rently outside of the Mandatory Health Plan (POS, Plan Obligatorio de Salud), here called non-POS, there will be a restructuring of the demand among POS and non-POS health services. The methodolog-ical approach used is the estimation of a discrete choice model that, based on the observed choices of claims and consumption of POS and non-POS services at the individual level, enables an estimation of the revealed preferences of individuals and a prediction of the new pref-erences after the health reform. Since the model is estimated by risk group (age, sex, and chronic diseases, or the lack thereof), it is possible to estimate the changes in cost and welfare by risk group. The results show that on average the expected increase in the cost of the new ben-efits plan is 16% compared to the current cost (POS plus non-POS), with a standard deviation of 7.10% among risk groups. However, con-sumer surplus is an average of 5.73 times greater than the increase in spending. This suggests that the new plan is very effective in gener-ating consumer surplus per additional spending unit. The results also identify the risk groups that will cost the most, most increase their well-being, and for whom the increase in well-being per additional spending unit will be the highest. Unlike a standard discrete choice model, the analysis conducted presents additional complications, as it is not possible to observe the utility of individuals for different choice alternatives (e.g., spending on non-POS services for individuals who choose only POS services is not observed). It is thus necessary to esti-mate these values. This difficulty and the calculation of welfare make for interesting theoretical developments in the article.
Keywords: Health Reform Colombia, New Benefits Plan, Discrete Choice Models.
Contents
1 Introduction 4
2 Non-POS Service Claim 5
3 A discrete choice model 5
4 Data 7
4.1 Estimation of spending on Non-POS . . . 8
5 Estimation of Parameters 9 6 Policy Evaluation 10 6.1 Spending . . . 11 6.2 Welfare . . . 11 7 Results 12 8 Conclusions 14
9 Apendix: Chronic Diseases 16 10 Apendix: Figures and Tables 17
1
Introduction
The current health plan in Colombia is defined by a list of services, proce-dures, and medications guaranteed by law to all insured persons. This plan is known as the Mandatory Health Plan (POS, Plan Obligatorio de Salud). However, if a physician decides that a patient requires a service, procedure, or medication that is not included on the list (these services are called non-POS) the patient should prepare for a long, paperwork-heavy process. He or she must submit a request that may or may not be endorsed by a Sci-entific Technical Committee (CTC, Comit´e T´ecnico Cient´ıfico) or as a last resort file a writ for the protection of constitutional rights. Ultimately a judge will determine whether or not the patient will receive the benefits re-quested. The disproportionate increase in non-POS service payments, called recoveries, either via the Scientific Technical Committee or via the protection of constitutional rights, is one of the main problems facing the Colombian public health system.
With the goal of better designing a benefits plan for Colombians, the Min-istry of Health has proposed unifying access to POS and non-POS services, keeping a much more selective negative (not included in the plan) list of services, procedures, and medications that are identifiable as services that definitely should not be included in the plan. In the new design the barrier to accessing what are currently called non-POS services will decrease signif-icantly.
To evaluate the systems implementation, it is necessary to calculate its cost and how it will affect consumer (patient) benefits. On the one hand, light-ened paperwork will generate an increase in the number of requests, and most likely an increase in the number of costly services approved. This will increase the countrys health spending. On the other hand, relaxation of costs will al-low individuals who require medication, and who were initially unwilling to incur claim costs, to change their decision. This will increase patient benefits.
This study uses a discrete choice model to predict patients’ decisions about whether to claim non-POS services or not. This will allow for an estimation of spending on health before and after the new design and the gain in patient surplus, which will enable a comparison of costs and benefits. The analysis tool will enable both an assessment of the redesigns impact on the entire
population and an assessment of its impact on vulnerable groups, such as the chronically ill or the elderly.
2
Non-POS Service Claim
There are two ways of accessing non-POS services. The first is a request to a Scientific Technical Committee (CTC) of the Health Provider Company (EPS, Empresa Prestadora de Salud) to which the patient belongs. This committee may approve the management of non-POS services and recover the value of the service from the Solidarity and Guarantee Fund (FOSYGA, Fondo de Solidaridad y Garant´ıa). This recovery does not necessarily corre-spond to 100% of the value, so EPSs might not have incentives to approve the service.
The second route is a writ for the protection of constitutional rights. To ac-cess this mechanism, the CTC request must have been rejected. The patient will have to submit a series of documents that prove he or she needs the service and cannot access it. Finally, a judge will determine whether or not the patient will receive the treatment.
Two problems can be identified in the current system design with respect to access to non-POS services. The first is the high cost that it generates for the patient. There is no doubt that the paperwork with the EPSs and the Colombian government requires time and patience. These costs can cause a patient who requires a medication to decide not to claim it. The second problem is that the person ultimately deciding whether or not to grant a service is a judge. It is possible that a judge, without medical knowledge, could give a patient a medication when there is a lower-cost one in POS, or it may happen that a judge rejects the request of a patient whose life depends on the administration of brand medication.
3
A discrete choice model
In order to estimate the expected cost of the new benefits plan, a discrete choice model was used with two alternatives: use of only POS services, and
use of POS and non-POS services. Since there was only a cross section of data (claim of POS and non-POS services during 2010), claim of non-POS services by individuals who only claim POS services is not observed. This is an additional challenge and it is addressed in the following section.
Formally, it is assumed that individualimust choose between claiming or not claiming non-POS services. Decision 1 will consist of claiming POS health-care services and not claiming non-POS healthhealth-care services. Decision 2 will consist of claiming POS healthcare services and claiming non-POS health services. It is easy to see that these decisions are mutually exclusive and exhaustive. 1 These two conditions allow for a utility to be associated with
each decision and for the adjustment of a discrete choice model.
Each of the decisions has a health benefit, but also generates costs for the individual. The costs of decision 1 are all the procedures and payments that the patient has to go through to be part of POS. The costs of decision 2 include the costs of decision 1 plus all the costs associated with claiming non-POS services. We say then that the utility of each decision will be given by
U1i =Health1i−CostsP OSi+Error1i (1)
U2i =Health2i−CostsP OS−CostsN ON P OS +Error2i
where Uji denotes the utility of individual i when making decision j and
Healthji denotes his or her health benefits after making decision j.
Errors can be interpreted in two ways. First, they represent all the factors affecting utility that are not included in the predictive variables. Second, they represent an irrationality component in the individual: there is a prob-ability that a person will not make the decision that maximizes his or her utility and this component is modeled by an error in the calculation of utility.
It is expected that the health benefits that an individual receives when choos-ing decision j depends positively on the spending that this individual would generate in the system. This is because procedures and services of higher
1All individuals in the base must contribute to the Mandatory Health Plan, whether
quality and variety generate both greater health benefits and a higher cost in the system. This dependence will be modeled linearly, firstly because any function can be approximated, locally, in this way, and secondly because it will lend itself to very interesting calculations in the levels of welfare of the population.
Summarizing the analysis, equation (??) will become
U1i =µ1+γP +β1Spending1i+ϵ1i (2)
U2i =µ2+γP +γN P +β2Spending2i+ϵ2i
whereγP and γN P are the costs of claiming POS and non-POS, respectively.
Spendingij will be the spending on health of decision j, ϵ1i and ϵ2i will be
errors with mean zero, and µ1,µ2 will be the means of the original errors.
The decision made by the individual depends only on whether U2 > U1 or
U2 < U1, so it is desirable to calculate the probability that U2 −U1 > 0.
Using (??) this value will be given by
P(U2i−U1i >0) =P(µ2 −µ1+γN P +β2Spending2i−β1Spending1i+ϵ2i−ϵ1i >0)
=P(ϵ2i−ϵ1i > µ1−µ2−γN P +β1Spending1i−β2Spending2i)
=F(µ1−µ2−γN P +β1Gasto1i−β2Gasto2i)
where F denotes the CDF of ϵ2i−ϵ1i
Finally, in a well-identified model, i.e., where spending is a good proxy of the health benefit, it is expected that µ2 =µ1. With this condition, we reach
P(U2i−U1i >0) =F(−γN P +β1Spending1i−β2Spending2i) (3)
and it will be possible to identify each of the constants using maximum likelihood if we know F.
4
Data
This analysis uses data on spending on POS and non-POS services during 2010 for more than a million Colombians who are part of the contributory
health regimen. We have the age and sex of each person. The database also indicates whether or not the individual suffers from a chronic disease, and if so, it indicates the diseases from which he or she suffers from a list of 36.2
Figure 1 shows spending on POS services by age, while Figure 2 shows spend-ing on non-POS for individuals who claim non-POS. Figure 3 shows the av-erage spending on non-POS for the general population.
It is observed that the average spending on POS and non-POS is slightly higher for newborns than for children. Spending remains relatively stable until age 45, when it begins to rise due to the health complications of the aging population. Spending increases until age 85, when there is a strong drop. This is because after a certain age patients do not undergo operations but rather receive inexpensive palliative care.
The spending on POS reported in the database is not suitable for making es-timates. This is because about 50% of the sample did not report information for the entire year, so the variable does not correspond to the annual spend-ing of the individual. To correct this problem the data are transformed by a rule of three that annualizes spending. The rule was applied to those who contributed for more than 30 days. If the contributory period was less than 30 days, the value of 30 days was given to this variable to avoid problems of exaggeratedly inflated annualized expenses.
4.1
Estimation of spending on Non-POS
To adjust a discrete choice model it is necessary to clearly define the op-tions of each individual. In particular, one must know the health spending that decision 1 and decision 2 will generate. These values can be calculated for individuals who choose decision 2 as they have spending in POS and in non-POS services. For an individual who chooses decision 1, the potential spending on non-POS services is unknown. This prevents an estimation of the model, so potential spending on non-POS must be calculated for these individuals.
2The complete list of classification of ICD10 codes in the 36 groups is available from
We will use the following model for spending on POS and non-POS services
SpendingN onP OSi|Xi =αSpendingP OSi|Xi+ηi (4)
where Xi is a vector of control variables. Xi includes age, sex, and chronic diseases of individual i.
The model indicates that after controlling for Xi, non-POS spending is pro-portional to POS spending. 3. This makes sense as there is a positive
corre-lation between POS spending and non-POS spending. Sick individuals, for example, will have a high spending on POS services, and on average, a high spending on non-POS services; on the other hand, a healthy individual will generate a low spending on POS services, and on average, a low spending on non-POS services. There is no need for a constant as it is expected that when POS spending is null, the individual will not be sick, and therefore, will not generate spending on non-POS services.
To control forXi the population is divided into groups. Each group is
deter-mined by an interval of age, gender, and chronic illness or lack of it. Equation (??) is estimated by OLS for each of the groups. After controlling for age, gender, and chronic disease, the constant α is independent of whether an in-dividual chooses decision 1 or 2. This implies that there will be no problems of selection bias in the estimation.
Using (??), the non-POS spending value is adjusted for those who do not report it. It is important to remember that in a linear regression the adjusted value for the dependent variable is an expected value. This makes sense since an individual does not know the health spending that will be generated in requesting non-POS services, but does know its prior expected value.
5
Estimation of Parameters
For the estimation of (??) the population will be divided into groups. Each group will be characterized by: an age range from a list of 12; gender; and
3A noiseη
a chronic disease or lack thereof. This gives a total of 720 groups. Within each group or cell a discrete choice model is adjusted. Each group then will yield a list of parameters. We will call this model Estimation by Cells.
There were a number of proposals for the estimation methodology. We believe estimation by cells is the best for three reasons. First, the costs of accessing non-POS services vary among groups and are not constant throughout the population.4 This makes it inappropriate to adjust a discrete choice model
like (??) for the entire base. Second, it is necessary that the assumption of iid error vectors be fulfilled in order to obtain efficient and consistent coef-ficients. This assumption is violated if we adjust a model to the entire base. 5.
Third, it is possible to use fixed effects or estimations based on mixed logits and GEV distributions to solve the problems which where just mentioned. However, these methods are used whenever sample size is a problem. Given the size of the database we are working with, dividing it into groups is not problematic. Moreover, the Cells methodology is much more general.
We believe that age, gender, type of disease, and health spending explains a significant portion of the utility generated by each decision the individual makes. This means the model is well-specified, and as such, a logit functional form forF is used as recommended by Train (2009). In 80% of the cells with more than 50 individuals the signs were as expected and all control variables were significant at 5% . Tables 5 and 6 report the results for two of the cells.
6
Policy Evaluation
The unification of POS and non-POS services in a single plan will facilitate paperwork and decrease costs of access to services not currently covered by the Mandatory Health Plan. From the standpoint of (??), the policy implies a reduction in γN P and therefore a change in the probability of choosing
de-cision 2.
4An elderly person with asthma may, for example, access non-POS services more easily
than a young person who does not suffer from chronic diseases.
5The diseases affecting the elderly population are much more varied than those affecting
the young population, so by controlling for spending, there is greater variance in utility error for the elderly than for the young.
If the costs of accessing non-POS services are reduced to a fractioncof what they were originally, the probability of choosing decision 2 will be given by
Pi =P(U2i−U1i >0) =F(−cγN P +β1Spending1i −β2Spending2i) (5)
wherePi is the probability of individualichoosing decision 2 when non-POS
costs have been reduced to a fraction c of what they were originally. Below it is described how from (??) it is possible to estimate the variation in health spending and the consumer surplus (welfare) of the entire population.
6.1
Spending
The expected spending of individual i will be given by
E[Spendingi] =PiSpendingi2 + (1−Pi)Spendingi1
so the expected spending of the entire population will be
E[T otalSpending] = n ∑ i=1 E[Spendingi] = n ∑ i=1 [PiSpendingi2+(1−Pi)Spendingi1] (6) where Pi is given by (??).
6.2
Welfare
In general, analyzing the change in welfare generated by a policy is compli-cated. Based on a discrete choice model one can calculate changes in utility levels, but these changes are, in principle, not comparable. Under certain cir-cumstances, however, it is possible to calculate the change in the consumer surplus generated by a policy. These assumptions perfectly fit our model. The methodology will follow Train (2009).
The individual i faces two decisions that represent a utility Ui1 = Vi1+ϵi1
and Ui2 = Vi2 + ϵi2. Here Vji denotes the observable part of the utility.
The individual’s utility will be that of the decision that generates the most benefit, i.e. Ui = max(Ui1, Ui2). Under the assumption of iid GEV errors
Small and Rosen (1981) showed that the expected value of the benefit will be
E[Ui] =E[max(Ui1, Ui2)] = ln(eVi1 +eVi2) (7)
If A is used to indicate values before and P is used to indicate values after the reform, the change in utility will be
E[∆Ui] =E[UiP]−E[UiA] =ln(eViP1 +eViP2)−ln(eViP1 +eViP2) (8)
Finally, when aiming to compare utility levels between individuals it is nec-essary to transform them into monetary units. If αi is the marginal utility of income, the change in utility transformed into monetary units will be given by E[CSi] = E[∆Ui] αi = ln(e ViP1 +eViP2)−ln(eViP1 +eViP2) αi (9)
This value will be the consumer surplus and will be denoted by CS. Train (2009) suggests how to calculate αi: In the estimation of the discrete choice
model the effect of government spending on the individual’s utility was calcu-lated. The estimated coefficient corresponds to the marginal effect of spend-ing on the utility, and it is an estimator of the marginal effect of a monetary change on the utility. It is possible to take, therefore, the estimated β1i as αi and calculate the surplus for each consumer.
7
Results
Calculations of the change in spending and consumer surplus when the re-form lowers the costs of accessing non-POS services in different proportions were made. The results are shown in Table 1. The deviations correspond to the variance between groups.
The advantage of the methodology used is that it enables a calculation of the changes in spending and surplus for each population group. It is then possible to identify which groups will benefit the most from the policy and which groups will have a greater increase in spending. Tables 3 and 4 show
groups that had a high, medium, and low increase in these categories.
The groups for which there is a greater proportional increase in consumer surplus with respect to spending were the individuals without chronic dis-eases, for at least two reasons. First, individuals with chronic diseases have a high probability of claiming non-POS services before the reform, so after the reform the number of individuals changing their preferences, i.e. beginning to claim non-POS services, is low compared to that of individuals without chronic diseases. Second, for an individual suffering from a chronic disease, costs of accessing non-POS are lower than for an individual who does not suffer from chronic diseases (a writ for protection of constitutional rights, for example, is more likely to be approved for the first individual than for the second). Therefore a reduction in non-POS costs has a greater impact on the non-chronic individual than on the chronic individual.
It is important to note that individuals who do not have chronic diseases have higher proportional changes in spending, but this does not imply higher changes in absolute spending. In fact the bulk of spending is, and will re-main, on individuals suffering from chronic diseases.
Another interesting quantity is the ratio between the change in the surplus and the change in spending. This factor shows how net health spending is multiplied to become a surplus. It is a very good measure of the efficiency of the policy. Table 2 shows the values of this ratio for the entire population and Table 5 shows values for a few select groups.
Note that for overall calculations the same weight was given to each of the groups. It may, however, be in the interest of the researcher or the govern-ment to give more importance to some groups than others. For example, less weight can be given to the surplus of individuals who do not suffer from chronic diseases, as they do not constitute a vulnerable section of the popu-lation.
8
Conclusions
The expected increase in health spending depends on how much the costs of accessing non-POS services are relaxed after the change in the system de-sign. As Table 1 shows, these increases are high in all cases. The increase in consumer surplus generated by the policy will also be high. Table 2 gives a measure of the efficiency of the policy when costs and benefits are com-pared. We see, for example, a 7-1 ratio between the change in surplus and the change in spending when costs are reduced to 25% of what they were originally. These values suggest that while the new benefits plan has a high cost to society, its benefits are high.
There is no room for an aggregate analysis of the policy, however, when the policymaker believes more importance should be given to certain segments of the population. For example, the government may seek to give more benefits to populations with chronic diseases or to children, rather than to adult pop-ulations without serious health problems. In this case, a general aggregate of the population is not useful. Fortunately, the methodology used in this study enabled an evaluation of policy performance in each of the risk groups. Moreover, a richer database that includes the location of the population, or non-chronic diseases, would allow the analysis to be focused on a specific section of the population.
The conclusion from the overall policy analysis is that it is very efficient. The conclusion from the policy analysis by risk groups is different: the effect of the new design on the behavior of the risk groups varies dramatically. While the policy change is efficient, some groups will benefit more than others (e.g. Epilepsy vs. Breast Cancer), and some groups will cost more than others (e.g. Diabetes vs. Arthritis). Table 1 shows the high deviation in the in-crease in spending and surplus between groups. It was shown, for example, that individuals who claim services but do not have chronic diseases greatly benefit from the new design, but whether the government wants to assume the high cost of this benefit for a non-vulnerable population is a regulatory question.
References
[1] Akaike, H. (1974) A new look at the statistical identication model,IEEE Transactionson Automatic Control 19(6), 716723.
[2] Hensher, D. and W. Greene (2003), The mixed logit model: The state of practice and warnings for the unwary, Transportation 30, 133176 [3] McFadden, D (1974) Conditional logit analysis of qualitative choice
be-havior. P. Zarembka, ed.,Frontiers in Econometrics, Academic Press, New York, pp. 105-142.
[4] Ruud, P. (2000), An Introduction to Classical Econometric Theory, Ox-ford University Press, New York
[5] Small, K. and H. Rosen (1981) Applied welfare economics of discrete choice models. Econometrica 49, 105-130.
[6] Train, K (2009) Discrete Choice Methods with Simulation. Cambridge University Press, pp. 11-174.
[7] Williams, H (1977) On the formation of travel demand models and eco-nomic evaluation measures of user benefits. Environment and Planning A 9, 285-344.
9
Apendix: Chronic Diseases
Below, the chronic-disease groups used based on classification CIE10:
Genetic and congenital abnormalities, arthritis, pyogenic arthritis and reac-tive arthritis, asthma, autoimmune disease, cancer insitu cervix, invasive cer-vical cancer, male genital cancer, breast cancer, cancer and skin melanoma, cancer digestive organs, respiratory system cancer, other cancer, other fe-male genital cancer, lymphatic cancer and related tissue therapy, cancer, diabetes, cardiovascular disease - hypertension, cardiovascular disease, other long lasting lung disease, kidney - chronic renal failure, renal failure - kidney failure other, kidney - other renal, kidney long lasting, AIDS-HIV, seizure syndromes (epilepsy), transplants, tuberculosis.
10
Apendix: Figures and Tables
Figure 1
0 20 40 60 80 100
GASTO EN POS POR EDAD
Edad Gasto POS 0 1000000 2000000 3000000 4000000
0 20 40 60 80 100 GASTO EN NOPOS GENTE NOPOS
Edad Gasto NoPOS 0 5000000 10000000 15000000
Figure 2
Figure 3
0 20 40 60 80 100
GASTO EN NOPOS POR EDAD
Edad Gasto POS 0 100000 200000 300000
Tables
Factor c Spending Deviation Surplus Deviation 0% 16.05% 7.10% 91.94% 120.21% 25% 7.36% 4.06% 53.17% 59.06% 50% 4.68% 2.52% 31.16% 31.91% 75% 2.40% 1.17% 13.78% 13.41%
Table 1: Overall increases in spending and surplus for different values of c
Factor c Ratio 0% 5.73 25% 7.22 50% 6.65 75% 5.74
Table 2: Overall ratio between change in Spending and change in Surplus for different values of c
Age Gender Disease Spending c= 25% Spending c= 50% 70-74 M NonChronic 14.75% 9.36% 19-44 M Arthritis 6.85% 4.49% 60-64 F Diabetes 3.79% 2.53%
Table 3: Changes in spending for some groups
Age Gender Disease Surplusc= 25% Surplus c= 50% 5-14 M NonChronic 293% 142% 5-14 F Epilepsy 41% 25% 15-18 F Breast Cancer 2.9% 1.6%
Table 4: Changes in surplus for some groups
Age Gender Disease Ratio c= 25% Ratio c= 50% 65-69 M Transplant 33.79 59.3 65-69 M Arthritis 10.17 9.54 55-59 F Tuberculosis 2.48 2.01
Table 5: Ratio between change in Spending and change in Surplus for differ-ent groups
Table 5: Logit Asthma, age group 8, men
Estimate Std. Error Z Value Pr(>|z|) (Intercept) -3.115 0.527 -5.900 3.610E-9 *** Spending1 -1.874E-6 6.306E-7 -2.971 2.971E-3** Spending2 2.111E-6 6.152E-7 3.431 6.02E-4***
Signif. codes: 0 ’***’ 0.001 ’**’ 0.01 ’*’ 0.05 ’.’ 0.1 ’ ’ 1
Null deviance: 107.855 on 99 degrees of freedom. Residual deviance: 55.601 on 97 degrees of freedom. AIC: 61.601
Number of Fisher Scoring iterations: 6
Table 6: Logit Genetic and congenital abnormalities,
age group 3, women
Estimate Std. Error Z Value Pr(>|z|) (Intercept) -2.954 0.1525 -19.376 ¡ 2e-16 *** Spending1 -1.111E-7 5.445E-8 -2.04 4.139E-2* Spending2 1.731E-7 4.118E-8 4.206 2.589E-5***
Signif. codes: 0 ’***’ 0.001 ’**’ 0.01 ’*’ 0.05 ’.’ 0.1 ’ ’ 1
Null deviance: 480.79 on 924 degrees of freedom Residual deviance: 409.57 on 922 degrees of freedom AIC: 415.57
